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If r and s are positive numbers, what are the coordinates...

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by BTGmoderatorLU » Sat Mar 10, 2018 2:06 pm
If r and s are positive numbers, what are the coordinates of the midpoint of line segment MNin the xy -plane?

(1) The coordinates of M are (r; 3-s).
(2) The coordinates of N are (3-r; s).

The OA is C.

I'm really confused by this DS question. Experts, any suggestion about how can I solve it? Thanks in advance.
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Source: — Data Sufficiency |
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by GMATinsight » Sun Mar 11, 2018 4:02 am
LUANDATO wrote:If r and s are positive numbers, what are the coordinates of the midpoint of line segment MNin the xy -plane?

(1) The coordinates of M are (r; 3-s).
(2) The coordinates of N are (3-r; s).

The OA is C.

I'm really confused by this DS question. Experts, any suggestion about how can I solve it? Thanks in advance.
Midpoint formula = (x1+x2 / 2, y1+y2 / 2)

So to find the midpoint we need the co-ordinates of both points M and N

Statement 1: The coordinates of M are (r; 3-s).
No information about the co-ordinate of point N hence
NOT SUFFICIENT

Statement 2: The coordinates of N are (3-r; s).
No information about the co-ordinate of point M hence
NOT SUFFICIENT

Combining the two statements

Co-ordinates of both M and N are known
Midpoints = (r+3-r/2 , 3-s+s/2) = (3/2, 3/2)

SUFFICIENT

Answer: option C
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by Vincen » Sun Mar 11, 2018 7:54 am
Hello LUANDATO.

Always to find the middlepoint of a segment, we need the coordinates of the two points. The only way to solve it here is using both statements. Now, the middlepoint of a segment is given by $$mp=\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right).$$ Now, using the statements we get that $$mp=\left(\frac{r+3-r}{2},\ \frac{3-s+s}{2}\right)=\left(\frac{3}{2},\frac{3}{2}\right).$$ Thus, we found the coordinates of the middlepoint of MN.

The correct answer is the option C.

I hope it helps.
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